The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  0  1  X  1  0  X  0  2  1  X  1  X  1  1  X  X  0  1  X  1  1  1  1  2  1  1  X
 0  X  0  X  0  0  X X+2  0  2  X  0 X+2  2 X+2 X+2  0  2  X  2  X  0 X+2 X+2  X X+2  2  0 X+2  X  0 X+2  0  0  0  2  X  0  X  2  X X+2  2 X+2 X+2  X  0  X X+2  0 X+2  0  X  2  2  2
 0  0  X  X  0 X+2  X  0  0  X  X  2  2 X+2  X  0  2  X  X X+2  0  0  2  X  0  X  0 X+2  0  0  X  0  0  X X+2  X  X  2  X  X X+2  2 X+2  2  0  2  X  X  X X+2  2  X  X  X X+2  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  0  2  0  2  0  0  0  0  2  2  0  2  0  2  2  0  2  0  2  0  0  0  0  0  2  2  2  0  0  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  0  0  2  2  2  2  2  2  0  0  2  2  0  0  2  2  0  0  2  0  2  0  0  2  0  2  2  0  0  2  2  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  2  2  0  2  0  0  0  2  2  2  0  0  0  2  0  0  2  2  0  2  2  0  2  0  0  2  0  2
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  2  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  2  2  0  2  2  2  0  2  0  0  2  2  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  0  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  2  0  2  2  0  2  2  2  2  2  0  2  0  2  2  0  2  2  2  0

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+102x^46+4x^47+273x^48+28x^49+465x^50+152x^51+663x^52+360x^53+1027x^54+480x^55+1178x^56+480x^57+965x^58+360x^59+692x^60+152x^61+392x^62+28x^63+213x^64+4x^65+95x^66+43x^68+23x^70+6x^72+3x^74+2x^76+1x^80

The gray image is a code over GF(2) with n=224, k=13 and d=92.
This code was found by Heurico 1.16 in 12 seconds.